Effects of cooperative intermolecular interactions on the electronic delocalization in mixed-valence biferrocenium trihalide compounds

Abstract

Intramolecular electron transfer in the mixed-valence complexes in the solid state shows qualitatively different behavior from that in an isolated complex. The ‘‘extra’’ electron in a given mixed-valence complex in the solid state may be localized at lower temperature and delocalized at higher temperature, even though the extra electron may be delocalized in the isolated molecule at any temperature. The solid state environment has an essential effect on the intramolecular electron-transfer rate in mixed-valence complexes. In order to clarify the mechanism of any possible environmental effects, a model is proposed for binuclear mixed-valence biferrocenium trihalides. A binuclear mixed-valence biferrocenium cation has two localized electronic states, [FeIIAFeIIIB] and [FeIIIAFeIIB], which are coupled to an out-of-phase combination of symmetric ligand–metal stretching modes, one on each metallocene unit. An intramolecular electronic interaction α induces the electron transfer between the two vibronic states of the mixed-valence cation. Each trihalide counterion is also mixed valence, also has two electronic states, [X−A- - -Y–XB] and [XA–Y- - -X−B], and an intramolecular electronic interaction β that induces charge oscillation in the trihalide anion. If the anion has only one molecular form, the charge oscillation due to the anion may be induced by another mechanism: Each anion may move between the two stable lattice positions as a whole. In addition to these two intramolecular interactions, cation–cation and cation–anion intermolecular interactions are considered in the context of a molecular field approximation. Energies and wave functions of the crystals are obtained. The electronic localization in the mixed-valence cation may be induced by the intermolecular interactions j, when j is large compared to α. The localized state becomes more unstable with increasing temperature, that is, the extra electron transfers more and more rapidly between the two iron ions in the cation, and the mixed-valence cation becomes delocalized at temperatures above a critical temperature TC. This electronic localization–delocalization transition occurs cooperatively and is a phase transition. The charge oscillation (X−A- - - Y–X−B ⇄ XA–Y - - -X−B) in the counteranions and/or the whole anion moving modulates the electron transfer rate in the cation. The present model consistently explains the various observed data from Mössbauer spectra, heat capacity measurements, x-ray crystallography, and infrared spectroscopy.